Offering accessible and nuanced coverage, Richard W. Hamming discusses theories of probability with unique clarity and depth. Topics covered include the basic philosophical assumptions, the nature of stochastic methods, and Shannon entropy. One of the best introductions to the topic, The Art of Probability is filled with unique insights and tricks worth knowing.
Table of Contents
Probability * Introduction * Models in General * The Frequency Approach Rejected * The Single Event Model * Symmetry as the Measure of Probability * Independence * Subsets of a Sample Space * Conditional Probability * Randomness * Critique of the Model Some Mathematical Tools * Permutations * Combinations * The Binomial DistributionBernoulli Trials * Random Variables, Mean and the Expected Value * The Variance * The Generating Function * The Weak Law of Large Numbers * The Statistical Assignment of Probability * The Representation of Information Methods for Solving Problems * The Five Methods * The Total Sample Space and Fair Games * Enumeration * Historical Approach * Recursive Approach * Recursive Approach * The Method of Random Variables * Critique of the Notion of a Fair Game * Bernoulli Evaluation * Robustness * InclusionExclusion Principle Countably Infinite Sample Spaces * Introduction * Bernoulli Trials * On the Strategy to be Adopted * State Diagrams * Generating Functions of State Diagrams * Expanding a Rational Generating Function * Checking the Solution * Paradoxes Continuous Sample Spaces * A Philosophy of the Real Number System * Some First Examples * Some Paradoxes * The Normal Distribution * The Distribution of Numbers * Convergence to the Reciprocal Distribution * Random Times * Dead Times * Poisson Distribution in Time * Queing Theorem * Birth and Death Systems * Summary Uniform Probability Assignments Maximum Entropy * What is Entropy? * Shannons Entropy * Some Mathematical Properties of the Entropy Function * Some Simple Applications * The Maximum Entropy Principle Models of Probability * General Remarks * Maximum Likelihood in a Binary Choice * Von Mises Probability * The Mathematical Approach * The Statistical Approach * When The Mean Does Not Exist * Probability as an Extension of Logic * Di Finetti * Subjective Probability * Fuzzy Probability * Probability in Science * Complex Probability Some Limit Theorems * The Biomial Approximation for the case p=1/2 * Approximation by the Normal Distribution * Another Derivation of the Normal Distribution * Random Times * The Zipf Distribution * Summary An Essay on Simulation
Richard W Hamming